Abstract

We use a new solution to heteroscedastic regression problem while avoiding so-called incidental parameters (inconsistency) problem by using recently discovered maps from time domain to numerical values domain and back. This involves a parsimonious fit for sorted logs of squared fitted residuals. Dufour [9] showed that inference based on Fisher’s pivot (dividing by standard errors) can be fundamentally flawed for deep parameters of genuine interest to policy makers. Hence, we use Godambe’s [12] pivot, which is always a sum of T items and asympotically subject to the central limit thory. We provide R functions to implement the ideas using the Phillips curve trade-off between inflation and unemployment for illustration. An Appendix discusses numerical methods to correct for general ARMA errors with an illustration of ARMA(4,3).